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Bulk Modulus of Compressibility of Diesel/Biodiesel/HVO Blends Magín Lapuerta,*,† John R. Agudelo,‡ Matthew Prorok,§ and André L. Boehman§ †

Escuela Técnica Superior de Ingenieros Industriales, Universidad de Castilla La-Mancha, Av de Camilo José Cela, 13071 Ciudad Real, Spain ‡ Facultad de Ingeniería, Universidad de Antioquia, Calle 67 #53-108, Medellín, Colombia § Department of Energy and Mineral Engineering, EMS Energy Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: The isothermal bulk modulus of compressibility is, together with viscosity and density, one of the properties affecting diesel injection processes. This property was measured by means of a specific apparatus that compresses a fuel sample in a high-pressure closed bottom capillary tube (a pycnometer) and by observing the height change in the column of fluid as pressure is increased over a range of pressures from 3 to 33 MPa. The bulk modulus of a conventional diesel fuel, a soybean oil derived biodiesel, and a hydrotreated soybean oil diesel fuel, together with that of their ternary blends, was measured. Water served as the calibration fluid, and measurements were made at 38 °C. All the fuels tested displayed substantially lower isothermal bulk modulus than water. There are observed differences between these fuel samples, with biodiesel displaying much lower compressibility than both the conventional diesel fuel and the hydrotreated oil. Although most of the blends showed bulk modulus values proportional to their volume fractions, some nonlinear effects were found when diesel fuel was involved in the blends, and particularly, a synergistic effect was found in blends with diesel and hydrotreated oil. An optimized correlation has been obtained to predict bulk modulus from the volume proportions of the three fuels tested.

1. INTRODUCTION The bulk modulus of compressibility of fuels affects their hydraulic behavior during the injection process. As the fuel is subjected to high pressure during the fuel injection process, the bulk modulus of compressibility describes how much the fuel will reduce in volume, referred to as dilatation. The variation in bulk modulus of compressibility with fuel composition and molecular structure is of interest, particularly in the case of alternative fuels, which may possess substantially different molecular structures than conventional petroleum-derived fuels. The bulk modulus of compressibility can be measured directly through observations of dilatation in fuels under pressure or determined from measurements of the speed of sound in the fluid, because the insentropic bulk modulus is directly related to the speed of sound in a fluid. Various researchers have investigated the compressibility of alternative fuels, with particular attention being paid to biodiesel and Fischer−Tropsch fuels because their bulk modulus of compressibility varies significantly from conventional diesel fuels. Many studies have reported advances in injection timing when biodiesel is used and retarded fuel injection timing when Fischer−Tropsch fuels are used.1−9 These studies have identified primarily that the advance in injection timing with biodiesel is related to increased bulk modulus of compressibility (and increased speed of sound), which leads to an earlier needle lift in pump-line-nozzle type fuel injection systems.2−5 The fuel viscosity has already been shown to influence fuel injection, with higher viscosity causing a more rapid pressure rise within the pump and thus as advance in injection timing.1,4 Modeling studies have highlighted the compressibility of the fuel as being the key property that influences injection timing.6,7 Consistent with these changes in injection timing, advances in injection timing with biodiesel and retarded injection timing with © 2011 American Chemical Society

Fischer−Tropsch fuels, NOx emissions tend to increase with the percentage of biodiesel content in a fuel and tend to decrease with the percentage of Fischer−Tropsch content in a fuel.8,9 In contrast, in common rail fuel systems, the rail pressure is constantly maintained at or near the desired injection pressure and fuel flows through the injector at a timing controlled electromechanically, rather than hydraulically. As such, the influence of the bulk modulus is not seen in the common rail fuel injection systems.10,11 P. W. Bridgman12 reviewed the methodologies for testing the compressibility of fluids and presented a summary of results that were available at that time for various fluids, including normal alkanes, iso-alkanes, alcohols, halogenated compounds, and water. Bridgman asserts that the compressibility of fluids at lower pressures is due to the consumption of free space between the loosely packed molecules. At higher pressures, the compressibility is less and is due to the compression of the molecules themselves and would be opposed by intermolecular repulsion. Thus, the bulk modulus should increase with increasing pressure as the resistance to further compression increases. Similar trends in the compressibility of hydrocarbons were observed by Cutler et al.,13 who considered a variety of pure hydrocarbons including normal alkanes from C12 to C18, branched alkanes, cycloalkanes, and aromatic compounds. They found that compressibility was greatest for normal alkanes, which have a less rigid structure, and decreased with increasing rigidity of molecular shape. Thus, compressibility increased as molecular structure varied from multiring aromatic to aromatic, to cycloalkane, to branched alkane, and to straight-chain alkane. Received: October 16, 2011 Revised: December 19, 2011 Published: December 20, 2011 1336

dx.doi.org/10.1021/ef201608g | Energy Fuels 2012, 26, 1336−1343

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Some additional trends were shown by Marcus and Hefter,14 who observed that both the length of the alkyl chains and the presence of oxygen functional groups decreased the compressibility. Among the oxygen groups, in carbon chains larger than three, hydroxyl groups decreased compressibility more than carbonyl groups and carboxylic groups (see Figure 1). Because

different molecular composition, as well as their effect on the fuel injection systems. These effects are especially important in fuel injection systems that rely on hydraulic force transferral to open a fuel injector, because injection timing, injection duration, or injection pressure might be affected by this property. However, no limits are specified for the bulk modulus of compressibility in the fuel quality standards, neither in automotive or aviation applications.

2. DEFINITIONS The isothermal bulk modulus of compressibility (B) can be defined as the inverse of the isothermal coefficient of compressibility. Because the distinction between isothermal bulk modulus and isentropic bulk modulus is only relevant for gases, only the isothermal one will be used here, and therefore, no subscript will be used: ∂p ∂v T (1) This can also be expressed as a function of the geometrical volume in a closed system with constant mass: B = −v

Figure 1. Effect of oxygen groups on the bulk modulus of linear hydrocarbons at ambient pressure and temperature. Data extracted from ref 14.

∂p ∂V T (2) There are two different numerical approaches for the estimation of the bulk modulus from a discrete collection of pressure−volume measurements under isothermal conditions:21 • Secant bulk modulus or average bulk modulus, based on the initial volume values, V0 (at atmospheric pressure, p0)

the bulk modulus is inversely related to the compressibility, the trend for bulk modulus would be to increase with increasing rigidity. Following Bridgman’s logic, the bulk modulus would increase with increasing density, because a more dense fluid would possess less free space to be consumed during compression. However, this does not occur for increasing length of the carbon chain (with increasing bulk modulus but decreasing density). Some studies have presented compressibility results with more practical diesel fuels. An example is provided by the work of Boehman et al.,15 who confirmed the strong correlation between fuel composition and molecular structure and the isothermal bulk modulus of compressibility. Vegetable oils with their triglyceride structure and biodiesel fuels with high levels of unsaturation (carbon carbon double bonds, which leads to highly nonlinear molecular structure) and with carboxylic groups displayed much higher bulk modulus than conventional and paraffinic diesel fuels. The lowest bulk moduli were associated with highly paraffinic fuels, such as the Norpar13 solvent (C11−C15 normal paraffins centered on C13), which has frequently been used in fuels research as a surrogate to represent jet fuels. Another example is the study by Martı ́nezBoza et al.,16 who observed that the bulk modulus of marine fuel-oils is higher and less sensitive to changes in pressure than that of distilled fuels. Some other researchers have also compared the compressibility of different diesel and biodiesel fuels, either from direct volume measurements17 or derived from measurements of sound velocity in the fuel.5,18−20 In all cases, the authors observed approximately linear increases of the bulk modulus with pressure and decreases with absolute temperature. They all observed higher bulk modulus values for biodiesel fuels than for diesel fuel with differences ranging from 120 to 200 MPa in the range of pressure up to 30 MPa. However, no study has yet been published with compressibility data for hydrotreated oil or their blends with other diesel fuels. These observations and general trends relating the isothermal bulk modulus of compressibility to the molecular structure and composition of a fuel can be used to anticipate and interpret the variations in compressibility between fuels with

B = −V

B = − V0

p − p0 V − V0

(3)

T

• Tangent bulk modulus or acoustic bulk modulus, based on the estimation of the instantaneous volume values from the measured data, Vi (at each pressure pi). Subscript i−1 indicates the previously recorded data.

V + Vi − 1 pi − pi − 1 B=− i 2 Vi − Vi − 1

T

(4)

Because the values obtained for the tangent bulk modulus are very noisy (as a result of their high sensitivity to measurement accuracy), secant bulk modulus is normally determined and used to compare the compressibility of liquids. However, it must be noted that the secant bulk modulus does not describe the physical behavior of a liquid in the actual pressure conditions but in the whole range from atmospheric pressure up to the actual pressure.

3. EXPERIMENTAL SECTION 3.1. Instrument. The methodology followed for the determination of the bulk modulus of fuels is based on the work of O’Brien.22 Measurements were carried out on an instrument that was developed for studying the viscosity and bulk modulus of hydraulic fluids that contained dissolved gases. This instrument permits the measurement of the reduction in volume of a fluid exposed to high pressures under isothermal conditions. The measurement equipment consists of a modified 21-R30 stainless Jerguson gauge that is capable of handling pressures up to 33 MPa. 1337


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A sample pressure cell with two quartz viewing windows allow for monitoring the sample. Each window glass has two gaskets, one on either side, to ensure a tight seal on the chamber. For pressures in the range 0−6.9 MPa, a direct connection to a helium gas cylinder provided the necessary pressure. For pressures above 6.9 MPa, a 4.5-L Aminco bomb was filled with helium, and oil was pumped into the bomb to achieve pressures up to 69 MPa. A constant temperature bath (Figure 2) kept the pressure cell at a temperature of 37.8 °C, the same

Table 1). The conventional ultralow sulfur diesel (ULSD) was a winter reference diesel supplied by Chevron Phillips Chemical.

Table 1. Methyl Ester Profile of Soybean-Oil Biodiesel methyl ester palmitic stearic oleic vaccenic linoleic linolenic

(% w/w) C16:0 C18:0 C18:1 (n9) C18:1 (n7) C18:2 C18:3

11.0 4.2 20.3 2.1 54.5 7.8

The main physical and thermochemical properties of all three pure fuels are shown in Table 2. Some of them are specifications of their

Table 2. Properties of the Pure Test Fuels properties density at 15 °C (kg/m3) kinematic viscosity at 40 °C (cSt) gross heating value (MJ/kg) lower heating value (MJ/kg)a % C (wt) % H (wt) % O (wt) % aromatics (wt) % olefins (wt) % paraffins (wt) sulfur content vp (ppm wt) molecular wt mean chemical formula stoichiometric fuel/ air ratiod initial boiling point (°C) cloud point (°C) cold filter plugging point (°C) lubricity (μm wear scar from HFRR, corrected) derived cetane number

Figure 2. Thermal bath with high pressure test chamber. temperature used by O’Brien. Bulk modulus was measured via a change in height within the pycnometer tube, as the pressure in the cell was varied. Distilled water was used as a calibration standard. A schematic of the layout is shown in Figure 3.

method EN ISO 12185 EN ISO 3104 UNE 51123 UNE 51123 ASTM D5291

HVO

biodiesel

diesel

775.8

885.9

843.8

3.53

5.78

3.67

46.97

39.84

45.28

43.73

37.30

42.54

84.84 15.16 0 0 0 100 0

77.15 11.89 10.96 0 0 0 -

87.14 12.86 0 28.8 3.4 67.8 10

216.4c C15.3H32.6

292.1c C18.8H34.4O2

199.9b C14.5H25.5

1/14.99

1/12.49

1/14.46

EN 3405

65

257

143

EN 23015 EN 116

3.3 −2

2.0 −3

−20 −27

EN ISO 12156

727

355

515

EN 15195

81.8

55.4

44.7

EN ISO 20884

a

Calculated from composition and gross heating value. bCalculated by AspenTech HYSYS software. cCalculated from speciation. dCalculated from elemental analysis. respective standards. Among these, only lubricity is out of specification for the diesel and HVO fuels, this meaning that lubricity additives should be included in both prior to commercialization. However, for this study, both biodiesel and HVO were tested without additives in order to provide a fair comparison. More details about the HVO composition can be obtained in ref 23. The biodiesel fuel is more dense and less volatile than both the diesel and HVO fuels. HVO has higher molecular weight than diesel fuel, although lower initial and final boiling points. However, in the intermediate range (from 20 to 80% in volume), distillation temperatures of diesel fuel are the lowest, as observed in distillation curves.23,24 Lower boiling points, especially in the high temperature range, are beneficial for a complete evaporation in the combustion chamber at low loads and at cold engine conditions (with peak pressures within the range 5−15 MPa). On the contrary, in the

Figure 3. Layout of the experimental installation. 3.2. Fuels and Blends. The hydrotreated oil (herein referred to as HVO) was manufactured from pure soybean oil (considered today as the most widely used feedstock among vegetable oils) by UOP (Universal Oil Products). Biodiesel fuel was also produced from soybean oil, and it was supplied by Peter Cremer North America (see fatty acid profile in 1338


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injection system (with pressures within the range 30−150 MPa), fuels will hardly evaporate but their compressibility may change as a function of pressure and temperature and to their proximity to saturation conditions. The characteristics shown here for both the HVO and biodiesel fuels correspond to one of the most typical feedstocks (soybean oil) and also to typical hydrotreating and transesterification reaction conditions. However, it must be acknowledged that different compositions and properties would be obtained if different feedstock or different reaction conditions were used, especially in the case of biodiesel fuels.25−27 The different properties of the three fuels tested make blending a way to design on-demand diesel fuels or to optimize the fuels for a specific diesel technology, depending on the injection system, after treatment systems, engine size, etc.24 From the opposite perspective, the electronic adjustment of the engine (or engine tuning) should be made considering the fuel used. From either viewpoint, a precise knowledge of the properties of the fuels or blends is essential. In the case of the bulk modulus of compressibility, the blend composition will mainly affect the injection system performance. As a means to limit these effects, a bulk modulus specification would be helpful. To compare the compressibility of binary blends, both HVO and biodiesel fuels were blended at 25, 50, and 75 volume percent with ULSD and between them. Some ternary blends were also tested, corresponding to 66.7% for each fuel and 16.7% for the two others, and finally a blend composed of one-third of each fuel. This makes a total of 16 tests, as shown in Figure 4.

closing valve A and opening valve B. Once oil was flowing, valve B was closed and the pump was turned off. Helium was allowed into the system by opening valve 14 and then opening valve 7. Opening valve 7 sent the pressurized helium to the gauge and sample. Valve 14 was closed at this point to save helium. The pump was used to achieve higher pressures. Valve C was opened to turn on the pump. Valve A was used to allow oil to flow into the bomb, pressurizing the helium gas. Once a desired measuring volume was achieved in the pycnometer, valve C was closed and the pressure was read from the gauge. 3.3.3. Releasing the Pressure. With valve C closed and the pump shut off, valves A and B were opened slightly to allow oil to flow back into the reservoir, thus relieving pressure in the system. Valve A was then closed quickly once helium began to escape through the valve. When all the oil was relieved from the system, valve 7 was closed to isolate the bomb, and valve 13 was opened to release the remaining pressure. The cell was then detached and the pycnometer removed for cleaning.

4. REPEATABILITY AND CALIBRATION A repeatability study was performed with diesel fuel. In this study, four sets of bulk modulus measurements (each one with increasing pressure) were made. As a result, a mean standard deviation of 25.7 MPa was obtained for the bulk modulus measurement, which can be identified with the standard measurement error. The calibration of the system was made with water and had two stages. In the first stage, the pressure gauge and the pycnometer volume readings were both calibrated. In the second stage, the resulting values for bulk modulus were compared with those obtained from the literature and from databases for distilled water. The pressure gauge used in the experiments was calibrated by comparison with pressure generated using a dead weight tester. The volume of the pycnometer was calibrated by weighing the mass of water added to reach each graduation on its outer scale and multiplying by the density of the distilled water. Three sources of data were used for the calibration of the system.22,28,29 The data for liquid water from R. W. Haywood28 were chosen because this is a widely recognized and used source. Because they only report values for 25 and 50 °C, the database from Kell and Whalley29 at 40 °C was also used. Finally, the data obtained from Ó Brien22 were also used because they were obtained with the experimental equipment that is the same as was used in the present work. The pressure and specific volume data for 25 and 50 °C (from Haywood) and for 40 °C (from Kell and Whalley) are shown in Figure 5. The regression correlations obtained (see equations embedded in Figure 5) were then derived to obtain the isothermal tangent bulk modulus at 25, 40, and 50 °C, following eq 1. The resulting values are shown in Figure 6, together with those directly given in ref 22. The results from the calibration made with distilled water are also presented in Figure 6. The results shown correspond to the secant or average bulk modulus. It can be checked that the values obtained (for 38 °C) are within the bulk modulus curves obtained from data reported by Haywood (for 25 and 50 °C), and slightly lower than those from Kell and Whalley (for 40 °C) and from Ó Brien (for 38 °C). Anyway, the differences are within the range of variation caused by measurement errors (see repeatability study mentioned above). Consequently, the system was considered to be properly calibrated.

Figure 4. Test matrix of fuel compositions. 3.3. Measurement Procedure. 3.3.1. Preparation of the Sample. First, the pycnometer was cleaned thoroughly. It was washed with acetone and flushed with distilled water, then placed in an oven at 110 °C for 20 min. Once cooled to room temperature, the pycnomter was washed with the sample fuel to remove any residual water. The pycnometer was then filled with the sample fuel to the 7.5 line. Care was taken to avoid creating bubbles anywhere in the sample, as these may impact the results of the test. The pycnometer was then carefully loaded into the test cell with a washer around its neck to prevent undesired movement of the pycnometer during handling of the test cell. The cell was submerged into the constant temperature bath until thermal equilibrium was reached. 3.3.2. Pressurizing the Sample and Measurement. The cell was connected to the apparatus via a high-pressure line and Swage-lock connection. At this point, all valves were closed. To purge the pressurizing oil, the pump was turned on by opening valve C (see schematic diagram in Figure 3) and a closed loop was created by 1339


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the proximity to the saturation conditions, and it is well-known that all liquids become more compressible as they get closer to saturation.12,29 Among the nonoxygenated fuels, the bulk modulus of diesel fuel is higher for pressures above 20 MPa, whereas the bulk modulus of HVO is higher for lower pressures. This shows that the contribution of the length of the carbon chain to the rigidity of the liquid may dominate at low pressure whereas the contribution of the aromatic content may dominate at high pressure. • All three fuels increase their bulk modulus as pressure increases. However, the rate of increase is much higher for diesel than for HVO and biodiesel, which exhibited similar rates. The higher rate of diesel’s bulk modulus with respect to that of biodiesel was also observed in some of the mentioned studies5,17,19 but cannot be clearly observed in others.15,18,20 The results of the average bulk modulus for binary blends are shown in Figures 8, 9, and 10. The following observations can be drawn from these figures:

Figure 5. Pressure−volume data for liquid water from refs 28 and 29.

Figure 6. Secant bulk modulus of water. Comparison between current results and data obtained or derived from the literature.22,28,29

5. RESULTS AND DISCUSSION The results of the average bulk modulus for the three fuels tested are shown in Figure 7. The following observations can be drawn from this figure:

Figure 8. Average bulk modulus for HVO/diesel blends.

Figure 7. Average bulk modulus for pure fuels.

Figure 9. Average bulk modulus for biodiesel/diesel blends.

• All the fuels tested displayed lower values of bulk modulus than water, meaning that the test fuels display higher compressibility than water, as expected. This is in agreement with results shown in the literature about the compressibility of hydrocarbons.12−14 The values obtained were of the same order as the results from other studies dealing with diesel fuels. • Biodiesel displayed higher bulk modulus than nonoxygenated fuels (diesel and HVO). This is in agreement with other authors' results5,15,17−20 and can be explained by the presence of carboxylic groups, the higher degree of unsaturation, and the longer mean carbon alkyl chain. Additionally, the lower volatility of biodiesel23,24 reduces

Figure 10. Average bulk modulus for HVO/biodiesel blends. 1340


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• Diesel/HVO blends (Figure 8) exhibited a synergistic effect, leading to higher values for bulk modulus in the case of blends with respect to the pure components. This synergistic effect reached a maximum for 25% HVO content. An explanation for this could lie in the increase in the diversity of hydrocarbon structures (aromatic rings, naphtenes, branched paraffins, linear paraffins, and a small amount of olefins), which could improve the molecular packing efficiency and consequently reduce the compressibility. The increasing rate of the bulk modulus with pressure for these blends remained between those observed for their pure components. • Diesel/biodiesel blends (Figure 9) exhibited no synergistic effect. However, small concentrations of biodiesel increased bulk modulus rapidly, indicating that the contribution of the ester group (together with those of the carbon number and the unsaturation degree) was dominant. Also, in this case, the increasing rate of the bulk modulus with pressure for these blends remained between those observed for their pure components. • HVO/biodiesel blends (Figure 10) exhibited no synergistic effect either, and in contrast to the case of diesel/biodiesel blends, the values obtained for bulk modulus were quite linear as a function of their volume concentration. The homogeneous origin of all the components (all coming from soybean oil despite the different transformation processes suffered) would lead to little additional molecular diversity and, thus, to no additional molecular interactions apart from those already existing in the biodiesel and HVO fuels. Finally, the results of the average bulk modulus for ternary blends are shown in Figures 11, 12, and 13. The following observations can be drawn from these figures:

Figure 13. Average bulk modulus for diesel-based ternary blends.

HVO lead to significant decreases in the bulk modulus. Such nonlinear decrease could again be explained with the decrease in the diversity of molecular structures and the increase in the amount of oil-derived components in the final blend. • Blends of biodiesel with a nonoxygenated blend (50% HVO in diesel) are shown in Figure 12. The bulk modulus was observed to increase with the biodiesel content, but in this case, no clear nonlinearities can be observed. Possibly, the increasing concentration of ester groups is somehow compensated by the increasing content of oil-derived moieties. • Blends of diesel with an oil-derived blend (50% biodiesel and 50% HVO) are shown in Figure 13. The decrease in the bulk modulus was not observed until a very high content of diesel fuel was reached in the blend. Such a strong nonlinearity was already observed in Figure 8 (HVO/diesel blends). In this case, however, no clear synergistic effect is reached. The explanation could be, again, the increase in diversity of molecular structures, in this case, being partly compensated by the coincidence of moieties with homogeneous origin. All these trends can be jointly observed in the ternary diagrams presented in Figure 14 for 10 and 25 MPa. At both pressures, all level curves tend to become mainly vertical, and they are monotonically ordered horizontally and almost equally spaced, which indicates that HVO and biodiesel do not contribute to substantial nonlinear effects. On the contrary, the curves appear to be disordered vertically, confirming that diesel fuel (located in the top corner) is involved in all the nonlinear effects observed. Another observation is that the level curves are closer at low pressure than at high pressure, meaning higher variations with changing composition. This is explained because the different pressure rates of the pure fuels make all bulk modulus values more uniform as the pressure is increased. The nonlinearities observed in bulk modulus when fuels were blended are in contrast with the results obtained for density, presented in ref 24, where no significant volume excess was found for any blend, proving that bulk modulus follows its own pattern independent of density.

Figure 11. Average bulk modulus for HVO-based ternary blends.

6. CORRELATION FOR THE PREDICTION OF THE BULK MODULUS OF BLENDS There are different proposals in the literature to simulate the increase of bulk modulus with pressure. However, it is generally accepted that for pressure values below 1000 bar, the linear equation is accurate enough.21 Consequently, the following

Figure 12. Average bulk modulus for biodiesel-based ternary blends.

• Blends of HVO with a B50 blend (50% biodiesel in diesel fuel) are shown in Figure 11. Small amounts of 1341


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Figure 14. Average bulk modulus ternary diagrams at 10 MPa (left) and 25 MPa (right). Level curves in MPa.

7. CONCLUSIONS

five-parameter correlation is proposed to predict the bulk modulus values as a function of the composition and the pressure:

The bulk modulus of compressibility was measured in a conventional diesel fuel, a soybean oil derived biodiesel, and a hydrotreated soybean oil diesel fuel, together with their ternary blends. As expected, all the fuels tested displayed substantially lower isothermal bulk modulus than water. Biodiesel showed much lower compressibility than both the conventional diesel and the hydrotreated oil, which can be explained by the presence of carboxylic groups, the higher degree of unsaturation, the longer mean carbon alkyl chain, and the lower proximity to saturation conditions. Although most of the blends showed bulk modulus values proportional to their volume fractions, some nonlinear effects were found when diesel fuel was involved in the blends, and particularly, a synergistic effect was found in blends with diesel and hydrotreated oil. This effect can be explained by the increase in the diversity of hydrocarbon structures, which could improve the molecular packing efficiency and reduce the compressibility. Opposing this effect, increasing the concentration of moieties with the same origin (as it occurs in biodiesel/HVO blends, both derived from soybean oil despite the different transformation processes suffered), and thus decreasing the molecular diversity, would reduce the molecular interactions and contribute to linearize the variations of bulk modulus in the blends. This can be visualized in the ternary diagrams presented for 10 and 25 MPa. These diagrams also show higher variations of bulk modulus with changing composition at low pressure. An optimized correlation for the prediction of bulk modulus as a function of the volume proportions and the pressure has confirmed that the nonlinear effects are concentrated in the diesel fraction and that the rate of increase with pressure is a linear function of the fuel fractions. The results presented are useful to predict and correct the effect of the fuel on the injection parameters in diesel engines (especially in those equipped with hydraulically controlled injection systems), such as the injection timing, with proven consequences on the NOx emissions.

3 B = a − bZHVO + c(Zbiodiesel − Zdiesel )

+ [dZdiesel + e(ZHVO + Zbiodiesel)]p

(5)

where Z represents the volume fractions. All the abovementioned nonlinear effects can be reasonably predicted by means of a single exponent (equal to 3) affecting the volume fraction of diesel fuel in the blends. Constants a, b, and c are used to predict the base values (intercept with zero-pressure axis), and constants d and e correspond to the rate of increase of bulk modulus with pressure. As can be checked, the rates for biodiesel and HVO have been identified in a single value, significantly lower than that for diesel fuel. The optimized values for these constants are listed in Table 3, and the correlation is displayed in Figure 15 (correlation coefficient R2 = 0.81). Table 3. Parameters for Predictive Correlation parameter

units

optimized value

a b c d e

MPa MPa MPa

1200 100 342 18 5

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +(34) 926295431. Fax: +(34) 926295361. E-mail: [email protected].

Figure 15. Prediction of the experimental bulk modulus of ternary blends by means of the proposed five-parameter correlation. 1342


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(20) Dzida, M.; Prusakiewicz, P. The effect of temperature and pressure on the physicochemical properties of petroleum diesel oil and biodiesel fuel. Fuel 2008, 87, 1941−1948. (21) Hayward, A. T. J. Compressibility equations for liquids: A comparative study. Br. J. Appl. Phys. 1967, 18, 965−77. (22) O’Brien, J. A. Precise measurement of liquid bulk modulus. M.S. Thesis, The Pennsylvania State University, University Park, PA, 1963. (23) Lapuerta, M.; Villajos, M.; Agudelo, J. R.; Boehman, A. L. Key properties and blending strategies of hydrotreated vegetable oil as biofuel for diesel engines. Fuel Process. Technol. 2011, 92, 2406−2411. (24) Lapuerta, M.; Rodriguez-Fernández, J.; Agudelo, J. R.; Boehman, A. L. Soybean oil derived biofuels for diesel engines. Biomass Bioenergy, submitted for publication. (25) Graboski, M. S.; McCormick, R. L. Combustion of fat and vegetable oil derived fuels in diesel engines. Prog. Energy Combust. Sci. 1998, 24, 125−64. (26) Knothe, G. Biodiesel and renewable diesel: A comparison. Prog. Energy Combust. Sci. 2010, 36 (3), 364−73. (27) Canakci, M.; Sanli, H. Biodiesel production from various feedstocks and their effects on the fuel properties. J. Ind. Microbiol. Biotechnol. 2008, 35 (5), 431−41. (28) Haywood, R. W. Thermodynamic Tables in SI (Metric) Units; Cambridge University Press: Cambridge, 1972. (29) Kell, G. S.; Whalley, E. The pVT properties of water I. Liquid water in the temperature range 0 to 150 °C and at pressures up to 1 kb. Philos. Trans. R. Soc., A 1965, 258, 565−617.

ACKNOWLEDGMENTS The authors gratefully acknowledge the Spanish Ministry of Education for the financial support to Prof. Lapuerta for his stay at the EMS Energy Institute, Pennsylvania State University (PR2010-0419), UOP for the donation of the HVO fuel, and the universities of Castilla-La Mancha, Antioquia, and Pennsylvania State, for supporting the authors' stays and for hosting them, respectively.

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REFERENCES

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